02856nam 22005175a 450 991015193910332120210304234502.03-03719-500-210.4171/000(CKB)3710000000953784(CH-001817-3)15-210304(PPN)178152803(EXLCZ)99371000000095378420210304j20031215 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierLogarithmic combinatorial structures: a probabilistic approach[electronic resource] /Richard Arratia, A. D. Barbour, Simon TavaréZuerich, Switzerland European Mathematical Society Publishing House20031 online resource (374 pages)EMS Monographs in Mathematics (EMM) ;2523-5192The elements of many classical combinatorial structures can be naturally decomposed into components. Permutations can be decomposed into cycles, polynomials over a finite field into irreducible factors, mappings into connected components. In all of these examples, and in many more, there are strong similarities between the numbers of components of different sizes that are found in the decompositions of `typical' elements of large size. For instance, the total number of components grows logarithmically with the size of the element, and the size of the largest component is an appreciable fraction of the whole. This book explains the similarities in asymptotic behaviour as the result of two basic properties shared by the structures: the conditioning relation and the logarithmic condition. The discussion is conducted in the language of probability, enabling the theory to be developed under rather general and explicit conditions; for the finer conclusions, Stein's method emerges as the key ingredient. The book is thus of particular interest to graduate students and researchers in both combinatorics and probability theory.Logarithmic Combinatorial StructuresProbability & statisticsbicsscAlgebrabicsscNumber theorybicsscProbability theory and stochastic processesmscNumber theorymscField theory and polynomialsmscProbability & statisticsAlgebraNumber theoryProbability theory and stochastic processesNumber theoryField theory and polynomials60-xx11-xx12-xxmscArratia Richard482210Barbour A. D.Tavaré Simonch0018173BOOK9910151939103321Logarithmic combinatorial structures277432UNINA